Simplify to lowest terms. $\dfrac{32}{24}$
Solution: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 32 and 24? $32 = 2\cdot2\cdot2\cdot2\cdot2$ $24 = 2\cdot2\cdot2\cdot3$ $\mbox{GCD}(32, 24) = 2\cdot2\cdot2 = 8$ $\dfrac{32}{24} = \dfrac{4 \cdot 8}{ 3\cdot 8}$ $\hphantom{\dfrac{32}{24}} = \dfrac{4}{3} \cdot \dfrac{8}{8}$ $\hphantom{\dfrac{32}{24}} = \dfrac{4}{3} \cdot 1$ $\hphantom{\dfrac{32}{24}} = \dfrac{4}{3}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{32}{24}= \dfrac{2\cdot16}{2\cdot12}= \dfrac{2\cdot 2\cdot8}{2\cdot 2\cdot6}= \dfrac{2\cdot 2\cdot 2\cdot4}{2\cdot 2\cdot 2\cdot3}= \dfrac{4}{3}$